Ch14.1 – Waves
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Ch14.1 – Waves. Wave – rhythmic disturbance, carries energy through matter or space. Transverse wave – wave vibrates perpendicular to the direction of travel -like a rope. Longitudinal wave (compression) – wave vibrates parallel to the motion of the wave, like a slinky.

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Ch14.1 – Waves

Wave – rhythmic disturbance, carries energy through matter or space.

Transverse wave – wave vibrates perpendicular to the direction of travel

-like a rope.

Longitudinal wave (compression) – wave vibrates parallel to the motion

of the wave, like a slinky.


Formulas: v = λ∙ f

f = 1/T

Freq units: Waves/sec (Hertz)

Period units: sec/wave

frequency

velocity

wavelength

Period (Time it takes for one wave to pass)

freq

(# of waves per second)


Ch14.1 – Waves

Wave – rhythmic disturbance, carries energy through matter or space.

Transverse wave – wave vibrates perpendicular to the direction of travel

- like a rope.

Longitudinal wave (compression) – wave vibrates parallel to the motion of the wave, like a slinky.

Formulas: v = λ∙ f

f = 1/T

Freq units: Waves/sec (Hertz)

Period units: sec/wave

Wavelength, (λ)

crest

Amplitude

trough

frequency

velocity

wavelength

Period (Time it takes for one wave to pass)

Freq

(# of waves

per second)


Ex1) A sound wave has a frequency of 262 Hz and a wavelength measured at 1.29 m.

a) What is the speed of the wave?

b) How long will it take the wave to travel the length of

a football field, 91.4m?

c) What is the period of the wave?

HW#1) A sound wave produced by a clock chime is heard 515 m away 1.50 s later.

a. What is the speed of sound of the clock’s chime in air?

b. The sound wave has a frequency of 436 Hz. What is its period?

c. What is its wavelength?


Ex1) A sound wave has a frequency of f = 262 Hz and a wavelength measured at λ = 1.29 m.

a) What is the speed of the wave?

b) How long will it take the wave to travel the length of a football field, 91.4m?

c) What is the period of the wave?

v=λ∙f

=(1.29m)(2621/sec)

=338m/s

d = v∙ t t = d/v = 91.4m/338m/s

= .27sec

T=? T=1/f = 1/2621/sec = .004sec

HW#1) A sound wave produced by a clock chime is heard 515 m away 1.50 s later.

a. What is the speed of sound of the clock’s chime in air?

b. The sound wave has a frequency of 436 Hz. What is its period?

c. What is its wavelength?

(v = λ∙f) or (v = d/t)?

v = 515m/1.5sec

= 343m/s

T = ? T = 1/f = 1/4361/sec = .002sec

v = λ∙ f

λ= v/f = 343m/s/436 1/sec = .8m


HW#7) A periodic longitudinal wave that has a frequency of 20.0 Hz travels along a coil spring. If the distance between successive compressions is .400 m, what is the speed of the wave?


HW#7) A periodic longitudinal wave that has a frequency of 20.0 Hz travels along a coil spring. If the distance between successive compressions is .400 m, what is the speed of the wave?

f = 20.0 Hz

v = λ∙ f

= (.4m) (20 1/sec) = 8 m/s

λ = .4m

v =


CH14 HW #1 1–7 20.0 Hz travels along a coil spring. If the distance between successive compressions is .400 m, what is the speed of the wave?

In class

A hiker shouts toward a vertical cliff 685 miles away. The echo is heard 4.00 sec later.

a. What is the speed of sound of the hiker’s voice in air?

b. The wavelength of the sound is .750 m. What is its frequency?

c. What is the period of the wave?

3. If you want to increase the wavelength of waves in a rope should you shake it at a higher or lower frequency?


CH14 HW #1 1–7 20.0 Hz travels along a coil spring. If the distance between successive compressions is .400 m, what is the speed of the wave?

In class

A hiker shouts toward a vertical cliff 685 miles away. The echo is heard 4.00 sec later.

a. What is the speed of sound of the hiker’s voice in air?

b. The wavelength of the sound is .750 m. What is its frequency?

c. What is the period of the wave?

3. If you want to increase the wavelength of waves in a rope should you shake it at a higher or lower frequency?

v = d/t = 685m/2s = 342.5m/s

(v = λ∙ f) f = v/λ = 342.5m/s/.75m = 456.7 Hz

T = 1/f = 1/456.7s-1 = .002s


CH14 HW #1 1–7 20.0 Hz travels along a coil spring. If the distance between successive compressions is .400 m, what is the speed of the wave?

In class

A hiker shouts toward a vertical cliff 685 miles away. The echo is heard 4.00 sec later.

a. What is the speed of sound of the hiker’s voice in air?

b. The wavelength of the sound is .750 m. What is its frequency?

c. What is the period of the wave?

3. If you want to increase the wavelength of waves in a rope should you shake it at a higher or lower frequency? Speed determined medium!

(v = λ∙ f)

v = d/t = 685m/2s = 342.5m/s

(v = λ∙ f) f = v/λ = 342.5m/s/.75m = 456.7 Hz

T = 1/f = 1/456.7s-1 = .002s

Shake Fast :

(Higher frequency)

shorter wavelength

Shake slow

(Low freq)

Longer wavelength


4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m?

5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength?

6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm?

7. In class

f = 5 waves/.1 sec = 50 Hz

λ = 1.2cm = .012m


4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m?

5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength?

6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm?

7. In class

v = λ∙ f = (.6m)(2.5s-1) = 1.5 m/s

f = 5 waves/.1 sec = 50 Hz

λ = 1.2cm = .012m


4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m?

5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength?

6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm?

7. In class

v = λ∙ f = (.6m)(2.5s-1) = 1.5 m/s

λ = v/f = 15.0m/s / 5.0s-1 = 3m

f = 5 waves/.1 sec = 50 Hz

λ = 1.2cm = .012m


4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m?

5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength?

6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm?

7. In class

v = λ∙ f = (.6m)(2.5s-1) = 1.5 m/s

λ = v/f = 15.0m/s / 5.0s-1 = 3m

1/sec

f = 5 waves/.1 sec = 50 Hz

λ = 1.2cm = .012m

v = λ∙ f

= (0.12m)(50s-1)

= .6m/s


Ch14.2 – Wave Behavior a frequency of 2.50 Hz and a wavelength of .600 m?

Incident wave – wave going in

Reflected wave – wave going out.

Reflection at a fixed boundary:

Reflection at a moveable boundary:

Passing from dense to less dense medium:

Passing from less dense to more dense medium:


Ch14.2 – Wave Behavior a frequency of 2.50 Hz and a wavelength of .600 m?

Incident wave – wave going in

Reflected wave – wave going out.

Reflection at a fixed boundary:

Reflection at a moveable boundary:

Passing from dense to less dense medium:

Passing from less dense to more dense medium:

Wave reflects 180o out of phase.

Crest comes back as a trough.

Wave reflects in phase.

Crest comes back as crest.

Part of wave continues upright,

part reflects off interface upright.

(Acts like moveable boundary.)

Part of wave continues upright,

part reflects off interface as trough.

(Acts like fixed boundary.)


Superposition of Waves a frequency of 2.50 Hz and a wavelength of .600 m?

Constructive interference – waves add energy

Ex1)

Ex2)

Destructive Interference – waves cancel energy

Ex3)

Ex4)

Ex5)


Superposition of Waves a frequency of 2.50 Hz and a wavelength of .600 m?

Constructive interference – waves add energy

Ex1)

Ex2)

Destructive Interference – waves cancel energy

Ex3)

Ex4)

Ex5)

Ch14 HW#2 8 – 11


Lab14.1 – Waves a frequency of 2.50 Hz and a wavelength of .600 m?

- due next day

- Ch14 HW#2 due at beginning of period


Ch14 HW#2 8-11 a frequency of 2.50 Hz and a wavelength of .600 m?

8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted?

9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor?

10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?


Ch14 HW#2 8-11 a frequency of 2.50 Hz and a wavelength of .600 m?

8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted?

Upright

9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor?

10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?


Ch14 HW#2 8-11 a frequency of 2.50 Hz and a wavelength of .600 m?

8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted?

Upright

9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor? Attached to wall

10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?


Ch14 HW#2 8-11 a frequency of 2.50 Hz and a wavelength of .600 m?

8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted?

Upright

9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor? Attached to wall

10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?




Ch15.1 – Sound the dashed line:

Sound waves are longitudinal waves.

- cause small pressure changes that are detected by ear.

- transmit through solids and liquids the same way.

- slower through denser materials, but faster if material is elastic.

Speed of Sound Through Various Media

Air (0oC) 331 m/s

*Air (20oC) 343 m/s (HW#1)

Water (25oC) 1493 m/s

Sea Water(25oC) 1533 m/s

Iron (25oC) 5130 m/s

Rubber (25oC) 1550 m/s

Ex1) A tuning fork produces a sound wave in air with a frequency

of 261.6 Hz. At a room temp the speed of sound is 343 m/s.

What is the wavelength?


Ch15.1 – Sound the dashed line:

Sound waves are longitudinal waves.

- cause small pressure changes that are detected by ear.

- transmit through solids and liquids the same way.

- slower through denser materials, but faster if material is elastic.

Speed of Sound Through Various Media

Air (0oC) 331 m/s

*Air (20oC) 343 m/s (HW#1)

Water (25oC) 1493 m/s

Sea Water(25oC) 1533 m/s

Iron (25oC) 5130 m/s

Rubber (25oC) 1550 m/s

Ex1) A tuning fork produces a sound wave in air with a frequency

of 261.6 Hz. At a room temp the speed of sound is 343 m/s.

What is the wavelength?

f = 261.6Hz

v = 343 m/s

λ = ?


Loudness – the dashed line:perception of sound intensity

Sound Level – measured in decibels

- measures the range from the faintest heard sound to the loudest

sounds.

- 10 dB increase is perceived jet engine – 110db

as being twice as loud. concert –

- 50,000 people yelling for 90 minutes

have the thermal energy ear damage – 70db

equivalent of a cup of coffee.

classroom –

this class –

faint sound – 0db

(threshold of hearing)

Pitch – related to frequency (High pitch = High Frequency)


Doppler Effect – an apparent change in the pitch of a sound.

(High pitch as approaches, low pitch as recedes.)

Velocity of sound is a constant

(determined by the medium!)

Wavelengths get scrunched (small λ)

Frequency goes up (v=λ.f)

Wavelengths expand (big λ)

Freq goes down. (v=λ.f)

Ch15 HW#1


Lab15.1 Speed of Sound with Cymbals sound.

- due tomorrow

- Ch15 HW#1 due at beginning of period


  • Ch15 HW#1 1 – 4 sound.

  • Find the frequency of a sound wave moving in air at room temperature with a wavelength of .667m.

  • f = ?

  • v = 343 m/s

  • λ = 0.667m

  • 2. The human ear can detect sounds with frequencies between 20 Hz and 16,000 Hz. Find the largest and smallest wavelengths the ear can detect, assuming that the sound travels through air with a speed of 343 m/s.

  • f = 20Hz f = 16,000Hz

  • v = 343 m/s v = 343 m/s

  • λ = ? λ = ?


  • Ch15 HW#1 1 – 4 sound.

  • Find the frequency of a sound wave moving in air at room temperature with a wavelength of .667m.

  • f = ?

  • v = 343 m/s

  • λ = 0.667m

  • 2. The human ear can detect sounds with frequencies between 20 Hz and 16,000 Hz. Find the largest and smallest wavelengths the ear can detect, assuming that the sound travels through air with a speed of 343 m/s.

  • f = 20Hz f = 16,000Hz

  • v = 343 m/s v = 343 m/s

  • λ = ? λ = ?


  • If you clap your hands and hear the echo from a distant wall 0.20 s later, how far away is the wall?

  • 4. What is the frequency of sound in air having a wavelength equal to the diameter of a 15 in. (38 cm) sub woofer speaker?

  • Of a 3.0 in (7.6 cm) tweeter? Use 343 m/s for speed of sound.

  • f = ? f = ?

  • v = 343 m/s v = 343 m/s

  • λ = 0.38m λ = 0.076m


  • If you clap your hands and hear the echo from a distant wall 0.20 s later, how far away is the wall?

  • 4. What is the frequency of sound in air having a wavelength equal to the diameter of a 15 in. (38 cm) sub woofer speaker?

  • Of a 3.0 in (7.6 cm) tweeter? Use 343 m/s for speed of sound.

  • f = ? f = ?

  • v = 343 m/s v = 343 m/s

  • λ = 0.38m λ = 0.076m

d = v.t = 343m/s. 0.10sec =


Ch15.2 – Physics of Music 0.20 s later, how far away is the wall?

Characteristic of 1 wavelength: crest

trough

Characteristic of 1 standing wave:

reflection perfectly overlaps crest crest

constructive destructive

interference interference

(antinodes) (nodes)


Ch15.2 – Physics of Music 0.20 s later, how far away is the wall?

Standing waves on strings – caused by constructive/destructive interference patterns that end on a node.


L 0.20 s later, how far away is the wall?

Fundamental frequency:

½λ fits L

λ = 2L

Anitnodes

1st harmonic:

1λ fits L

λ = L

Nodes

2nd harmonic:

1½ λ fits L

λ = 2/3L

String instruments have different lengths and thicknesses of strings

that can vibrate at different frequencies (diff pitches).


Ex1) A guitar string is 64 cm long. If the speed of sound is 343m/s, what is the lowest possible frequency the string can hold?

Ex2) A 256 Hz “C” note is played on a piano. If the speed of sound is 343m/s ,

what is the length of the string?

Ex3) A banjo has a string length of 80 cm. if v = 343m/s , what is the frequency

of the 1st harmonic?


Ex1) A guitar string is 64 cm long. If the speed of sound is 343m/s, what is the lowest possible frequency the string can hold?

fund freq:

½λ=L

½λ = 0.64m

λ = 1.28m

Ex2) A 256 Hz “C” note is played on a piano. If the speed of sound is 343m/s ,

what is the length of the string?

fund freq:

½λ=L

f = 256Hz

L = ½λ= 0.67m

Ex3) A banjo has a string length of 80 cm. if v = 343m/s , what is the frequency

of the 1st harmonic?

1st harmonic:

1λ fits L

λ = 0.80m

Ch15 HW#2 5 – 8


  • Ch15 HW#2 5 – 8 343

  • A mandolin string is 105 cm long. If it’s a cold day, the speed of sound is

  • 335 m/s, what is the lowest possible frequency the string can hold?

  • fund freq:

  • ½λ = L

  • ½λ = 1.05m

  • λ = 2.10m

  • A 512 Hz “C” note is played on a piano. If the speed of sound is 343 m/s,

  • what is the length of the string?

  • fund freq:

  • ½λ = L

  • f = 512Hz

  • 7. A banjo has a string length of 80 cm. If v = 343 m/s, what is the frequency of the second harmonic?

  • 1½ λfits L

  • λ = 2/3 L

  • λ = 2/3(0.8m)

  • λ = 0.53m


  • Ch15 HW#2 5 – 8 343

  • A mandolin string is 105 cm long. If it’s a cold day, the speed of sound is

  • 335 m/s, what is the lowest possible frequency the string can hold?

  • fund freq:

  • ½λ = L

  • ½λ = 1.05m

  • λ = 2.10m

  • A 512 Hz “C” note is played on a piano. If the speed of sound is 343 m/s,

  • what is the length of the string?

  • fund freq:

  • ½λ = L

  • f = 512Hz

  • ½λ = L =

  • 7. A banjo has a string length of 80 cm. If v = 343 m/s, what is the frequency of the second harmonic?

  • 1½ λfits L

  • λ = 2/3 L

  • λ = 2/3(0.8m)

  • λ = 0.53m




Ch15.3 – Waves in Pipes m/s, what is the frequency of the first harmonic?

Reminder: standing wave:

Closed Pipes – antinode at open end, node at closed end.

Fundamental Freq: 1st Harmonic:

Ex1) A 512 Hz is held above a closed pipe 16 cm long when sound resonates. What is the speed of sound?


Ch15.3 – Waves in Pipes m/s, what is the frequency of the first harmonic?

Reminder: standing wave:

Closed Pipes – antinode at open end, node at closed end.

Fundamental Freq: 1st Harmonic:

¼ λ fits L ¾λ fits L

λ = 4L λ = 4/3 L

Ex1) A 512 Hz tuning fork is held above a closed pipe 16 cm long when sound resonates. What is the speed of sound?


Ch15.3 – Waves in Pipes m/s, what is the frequency of the first harmonic?

Reminder: standing wave:

Closed Pipes – antinode at open end, node at closed end.

Fundamental Freq: 1st Harmonic:

¼ λ fits L ¾λ fits L

λ = 4L λ = 4/3 L

  • Ex1) A 512 Hz tuning fork is held above a closed pipe 16 cm long when sound resonates. What is the speed of sound?

  • ¼ λ fits L v = λ.f

  • λ = 4(.16m) = (0.64m)(512 s-1)

  • λ = 0.64m = 328 m/s


Spacings m/s, what is the frequency of the first harmonic? – resonance will occur again when the closed pipe is lengthened every 1/2λ.

Ex2) A 392 Hz tuning fork resonates sound waves in closed pipes that

are 21 cm long and 63 cm. What is the speed of sound?


Spacings m/s, what is the frequency of the first harmonic? – resonance will occur again when the closed pipe is lengthened every 1/2λ.

Ex2) A 392 Hz tuning fork resonates sound waves in closed pipes that

are 21 cm long and 63 cm. What is the speed of sound?

21cm

63cm

½λ = (one football)

= 63 – 21 = 42cm

λ = 0.84m

f = 392Hz

v = λ.f

= (0.84m)(392s-1)

= 329 m/s


Open Pipe – m/s, what is the frequency of the first harmonic?open at both ends (antinodes)

HW#12) A bugle can be thought of as an open pipe as shown.

If a bugle were straightened out, it would be 2.65 m long. If the speed

of sound is 343 m/s, find the lowest frequency that is resonant in a bugle.

Find the next higher-resonant frequency in the bugle.


Open Pipe – m/s, what is the frequency of the first harmonic?open at both ends (antinodes)

Fund freq: 1st harmonic:

½λ fits L λ fits L

λ = 2L λ = L

HW#12) A bugle can be thought of as an open pipe as shown.

If a bugle were straightened out, it would be 2.65 m long. If the speed

of sound is 343 m/s, find the lowest frequency that is resonant in a bugle.

Find the next higher-resonant frequency in the bugle.

½λ = L

λ = L

Ch15 HW#3 9 – 13


Lab15.2 – Sound Barrier m/s, what is the frequency of the first harmonic?

- due tomorrow

- Ch15 HW#3 due at beginning of period


Ch15 HW#3 9 – 13 m/s, what is the frequency of the first harmonic?

9. a 440Hz tuning fork is held above a 19cm pipe.

What is speed of sound?

10. 440Hz tuning fork resonates in helium at 55cm.

What is the speed of sound?

11. Unknown tuning fork, resonates at spacings of 20.2cm.

Find f.

13. Sax is 65cm long. Find lowest freq. 20.2cm


  • Ch15 HW#3 9 – 13 m/s, what is the frequency of the first harmonic?

  • 9. a 440Hz tuning fork is held above a 19cm pipe.

  • What is speed of sound?

  • ¼ λ fits L v = λ.f = (0.76m)(440Hz)

  • λ = 0.76m =

  • 10. 440Hz tuning fork resonates in helium at 55cm.

  • What is the speed of sound?

  • ¼ λ fits L v = λ.f = (2.20m)(440Hz)

  • λ = 2.20m =

  • 11. Unknown tuning fork, resonates at spacings of 20.2cm.

  • Find f.

  • ½λ = 20.2cm

  • λ = .404m

  • 13. Sax is 65cm long. Find lowest freq. 20.2cm

  • ½λ = 65cm

  • λ = 1.30m


Ch14,15 Rev 1 – 13 m/s, what is the frequency of the first harmonic?

Two ropes are attached. A wave reaches the boundary of the ropes as shown. The wave continues as shown. Which rope is more dense?

2. When 2 waves interfere, is there a loss of energy in the system?

A standing wave is on a string as shown. There are points where it can be touched without disturbing its motion. Explain. How many of these points exist?

4. What happens to the period of a wave as the frequency increases?

5. What happens to the wavelength of a wave as the frequency increases?


Suppose you make a single pulse on a stretched spring. How much energy is required to make a pulse with twice the amplitude?

7. The Sears Tower sways back and forth with a frequency of about

0.10 Hz. What is its period?

8. The frequency of yellow light is 5.0 x 1014 Hz. Find the wavelength of yellow light. (v = 3 x 108 m/s)


9. Sketch the result of the three cases shown, when the centers of the

two wave pulses lie on the dashed line so that the pulses exactly overlap.

a.

b.

c.

You hear the sound of the firing of a cannon 6.0 s after seeing the flash. How far are you from the cannon?

If you shout across a canyon and hear an echo 4.0 s later, how wide is the canyon?


12. A sound wave has a frequency of 9800 Hz and travels along a steel rod. Is the distance between compressions, or regions of high pressure,

is .580 m, what is the speed of the wave?

13. Sound with a frequency of 261.6 Hz travels through water at a speed of 1435 m/s. Find the wavelength in water.


Bonus) In the lab yesterday, a tuning fork with a freq of 512Hz resonated

in a tube of length 16cm. What is the speed of sound?

At what length would it resonate again?

Bonus) Air is blown thru a tube open at both ends, resonating at a fundamental frequency of 256Hz. If the tube is 70cm long, what is the speed of sound there?


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