Question

A student standing in a canyon yells "echo", and her voice produces a sound wave of frequency of f = 0.54 kHz. The echo takes t = 2.1 s to return to the student. Assume the speed of sound through the atmosphere at this location is v = 320 m/s.

f = 0.54 kHz
t = 2.1 s
v = 320 m/s
A) Input an expression for the distance, d, the canyon wall is from the student.
d=
B) How many wavelengths are between the student and the wall?
N=

Answer 1

The distance between the student and the canyon wall is 336 m, and there are approximately 0.567 wavelengths between them.

Step-by-step explanation:

To find the distance, d, between the student and the canyon wall, we can use the formula:

d = v * t / 2

where v is the speed of sound and t is the time it takes for the echo to return. Plugging in the values, we have:

d = 320 m/s * 2.1 s / 2 = 336 m

To find the number of wavelengths between the student and the wall, we can use the equation:

N = d / λ

where λ is the wavelength of the sound wave. We can find the wavelength using the formula:

λ = v / f

Plugging in the values, we get:

λ = 320 m/s / 0.54 kHz = 592.59 m

Then, plugging the values into the equation, we have:

N = 336 m / 592.59 m = 0.567 wavelengths