A physics student drops a vibrating 440-hz tuning fork down the elevator shaft of a tall building. when the student hears a frequency of 400 hz, how far has the tuning fork fallen?

A wave's frequency changes in response to an observer moving in respect to the wave source, which is known as the Doppler effect or Doppler shift. It has the name of Christian Doppler, an Austrian physicist who first reported the phenomena in 1842.

Mathematically it is written as;

[tex]f' = \frac{(v+v_{0}) }{(v -v_{s}) } f[/tex]

1. Using doppler effect,

u = 340(440/440-1) m/s

u = 34m/s

Therefore, the speed of the source is 34m/s.

2. y = [tex]u^{2}[/tex]/2g

y = [tex]34^{2}[/tex]/2×9.8

y = 58.92m

So, [tex]t_{1}[/tex] = u/g (Using u obtained above from Doppler effect)

[tex]t_{1}[/tex] = 34/9.8

[tex]t_{1}[/tex] = 3.466s

Therefore, the location of the source at that time ([tex]t_{1}[/tex]) is 3.466s.

3. [tex]t_{2}[/tex] = 58.92 / 340

[tex]t_{2}[/tex] = 0.173s.

Therefore, the time ([tex]t_{2}[/tex]) for sound to travel 58.92 m is 0.173s.

4. d = [tex]\frac{1}{2}gt^{2}[/tex]

d = [tex]\frac{(9.81)(3.639^{2}) }{2}[/tex]

d = 65m.

Therefore, the distance the source has fallen in time ([tex]t_{1} + t_{2}[/tex]) is 65m.

The complete question is: A physics student drops a vibrating 440-hz tuning fork down the elevator shaft of a tall building. when the student hears a frequency of 400 hz, how far has the tuning fork fallen?

1.Find the speed of the source from Equ. 15-332.

2.Find the location of the source at that time ([tex]t_{1}[/tex])

3. Find the time ([tex]t_{2}[/tex]) for sound to travel 58.92 m.

4.Find the distance the source has fallen in time ([tex]t_{1} + t_{2}[/tex])

Learn more about Doppler effect here:

https://brainly.com/question/28106478

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