Sound Waves Frequency Calculation Help

[nubey1]

Homework Statement

A loudspeaker at the origin emits sound waves on a day when the speed of sound is 340 m/s. A crest of the wave simultaneously passes listeners at the coordinates (38m,0m) and (0m,29m). What are the lowest two possible frequencies of the sound?

Homework Equations

D(x,t)=Asin(kx-wt+$$\phi$$)
D(y,t)=Asin(kx-wt+$$\phi$$)

The Attempt at a Solution

I do not know where to start with this problem. I received some advice from the TA, but I am still confused.

 

[lanedance]

assume the wave eminates spherically from the speaker

the fact that they are different distances from the speaker means the listeners both hear different crests at the same time...

think about distances...

how apart are crests in the wave...

how far is each listener form the speaker...

 

[nlightner]

I would start by breaking down the given information into relevant equations and variables. The first equation, D(x,t)=Asin(kx-wt+\phi), represents the displacement of a sound wave in the x-direction. The second equation, D(y,t)=Asin(kx-wt+\phi), represents the displacement in the y-direction. In both equations, A represents the amplitude of the wave, k represents the wave number, w represents the angular frequency, and phi represents the phase shift.

Using the given coordinates, we can determine the distance between the two listeners as 38m in the x-direction and 29m in the y-direction. This distance will be equal to the wavelength of the sound wave, as it is the distance between two consecutive crests of the wave. We can also determine the time it takes for the wave to travel from the origin to each listener, which will be equal to the period of the wave.

Now, we can use the equation v=λf to calculate the frequency of the sound wave. The speed of sound, v, is given as 340 m/s, and the wavelength, λ, is equal to the distance between the two listeners. By rearranging the equation, we can solve for the frequency, f.

f = v/λ = 340 m/s / 38m = 8.95 Hz

This is the lowest possible frequency of the sound wave, as it is the frequency at which the distance between the two listeners is equal to one full wavelength. However, this is not the only possible frequency. As sound waves can have different wavelengths, there could be other frequencies at which the distance between the two listeners is equal to an integer multiple of the wavelength.

To find these other possible frequencies, we can use the equation f = n(v/λ), where n is an integer representing the number of wavelengths between the two listeners. For example, if n=2, the distance between the two listeners would be equal to two full wavelengths, giving us a frequency of 17.9 Hz. Similarly, if n=3, the frequency would be 26.9 Hz.

Therefore, the lowest two possible frequencies of the sound wave are 8.95 Hz and 17.9 Hz.