Sound Wave Problem: Frequency of Note in Amphitheater

In summary, the conversation discusses how a handclap in an amphitheater produces a periodic series of pulses that create a played note. The question is to find the frequency of the perceived note, given the width of the terraces and the speed of sound in air. The solution involves understanding the movement and speed of the sound waves, the path length difference between returning pulses from adjacent terraces, and using relevant equations to calculate the frequency. The final answer is 177.35 Hz.
  • #1
i_hate_math
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Homework Statement


A handclap on stage in an amphitheater sends out sound waves that scatter from terraces of width w = 0.967 m (see the figure). The sound returns to the stage as a periodic series of pulses, one from each terrace; the parade of pulses sounds like a played note. (a) Assuming that all the rays in the figure below are horizontal, find the frequency at which the pulses return (that is, the frequency of the perceived note). (b) If the width w of the terraces were smaller, would the frequency be higher or lower? (Note: Assume the speed of sound in air = 343 m/s.)

Homework Equations


S = Sm*cos(kx-vt) maybe?

The Attempt at a Solution


I am clueless for this question, can someone suggest an approach? I don't know what the theory id behind this
Thanks
 

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  • #2
Sound from a single source is bouncing off of a series of surfaces whose distances from the source are separated by a regular fixed increment.

What's moving? How fast does it move? What's the path length difference for sound returning from adjacent terraces? What then is the time difference between returning pulses from adjacent terraces? Knowing the time interval between return pulses, what's the frequency?

Surely you can quote relevant equations that pertain to velocity, distance, and time? How about period and frequency?

You should be able to make an attempt.
 
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  • #3
gneill said:
Sound from a single source is bouncing off of a series of surfaces whose distances from the source are separated by a regular fixed increment.

What's moving? How fast does it move? What's the path length difference for sound returning from adjacent terraces? What then is the time difference between returning pulses from adjacent terraces? Knowing the time interval between return pulses, what's the frequency?

Surely you can quote relevant equations that pertain to velocity, distance, and time? How about period and frequency?

You should be able to make an attempt.
The sound waves are moving at 343m/s, the time difference is T=w/343 = 0.967/343=0.002819...
Hence the frequency is f=1/T=354.705274 Hz
Does that look right?
 
  • #4
i_hate_math said:
The sound waves are moving at 343m/s, the time difference is T=w/343 = 0.967/343=0.002819...
Hence the frequency is f=1/T=354.705274 Hz
Does that look right?
Almost. Take a close look at the extra distance traveled by the reflected waves from successive terraces. Remember, the waves are reflected so they travel the same path forward and back:
upload_2016-5-7_5-42-30.png
 
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  • #5
gneill said:
Almost. Take a close look at the extra distance traveled by the reflected waves from successive terraces. Remember, the waves are reflected so they travel the same path forward and back:
View attachment 100394
Oh right! Shame on me for not seeing that.
It should be T=2w/343 = 2*0.967/343=0.0056384..
and f=1/T=177.35 Hz
 
  • #6
That looks good.
 
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  • #7
gneill said:
That looks good.
Thank you very much for your help!
 

1. What is a sound wave?

A sound wave is a type of mechanical wave that travels through a medium, such as air or water, and carries energy from one place to another. It is created by the vibration of an object, such as a musical instrument, and is perceived by the human ear as sound.

2. How is the frequency of a sound wave determined?

The frequency of a sound wave is determined by the number of vibrations or cycles per second. It is measured in hertz (Hz) and is directly related to the pitch of the sound. A higher frequency corresponds to a higher pitch, while a lower frequency corresponds to a lower pitch.

3. What is the relationship between frequency and wavelength?

The frequency and wavelength of a sound wave are inversely proportional to each other. This means that as the frequency increases, the wavelength decreases and vice versa. This relationship is described by the equation: speed of sound = frequency x wavelength.

4. How does the shape and size of an amphitheater affect sound waves?

The shape and size of an amphitheater can greatly affect the propagation of sound waves. The curved shape of an amphitheater helps to reflect and focus sound waves, resulting in better acoustics and amplification of sound. The size of the amphitheater also affects the reverberation time, with larger spaces having longer reverberation times.

5. How can the frequency of a note be calculated in an amphitheater?

The frequency of a note in an amphitheater can be calculated by using the equation: frequency = speed of sound / wavelength. The speed of sound can be determined by the medium through which the sound wave is traveling, and the wavelength can be measured by the distance between two consecutive peaks or troughs of the wave.

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