Two speakers, A and B, are emitting identical, synchronized (in-phase) sound waves at 240kHz. A person standing a point C hears a relatively loud sound. She then starts walking towards point D, and notices the sound gets quieter, reaching a minimum when she arrives at D. The distance from speaker A to D is 3.10m. The distance from speaker B to D is 2.40m.
a) From the information given above,what is the wavelength of the sound?
b) From the information given above, what is the speed of the sound?
wavelength = .96 m
speed = 345.6 m/s
To find the wavelength of the sound, we can use the formula:
wavelength = speed of sound / frequency
The frequency of the sound is given as 240 kHz, which we need to convert to Hz:
frequency = 240 kHz = 240,000 Hz
Now, we need to find the speed of sound. To do this, we can use the formula:
speed of sound = distance / time
Since we do not have information about the time taken, we need to find an alternative way to determine the speed of sound.
Given that the person moving from C to D hears a minimum in sound intensity, this suggests that there is a phase difference between the waves from speakers A and B at point D. This phase difference occurs due to a path length difference between the two speakers.
The path length difference between the two speakers is:
Δd = distance from B to D - distance from A to D
Δd = 2.40 m - 3.10 m
Δd = -0.70 m
Note that a negative value indicates the relative positions of the speakers.
Now, we can use the phase difference to determine the wavelength using the formula:
wavelength = (speed of sound × path length difference) / (2π)
To calculate the speed of sound, we need to determine the wavelength. However, to determine the wavelength, we need the speed of sound. This is a bit of a catch-22 situation.
Therefore, with the information given, it is not possible to directly calculate the speed of sound or the wavelength. Additional information, such as the frequency at which the sound intensity from the two speakers changes, is needed to solve the problem.