Question

In: Physics

At the beach, some waves with wavelength of 100 m propagate towards the shore at a...

At the beach, some waves with wavelength of 100 m propagate towards the shore at a speed of 12.5 m/s. (c) Does the engine sound higher- or lower-pitched to someone standing on the shore, compared with the experience of people on the boat?

(a) Calculate the frequency that boat anchored near shore bobs up and down as the waves roll in.

(b) At what frequency the boat would bob up and down with if it were headed away from the shore at a speed of 4.8 m/s?

(c) At what frequency the boat would bob up and down with if it were headed toward the shore at a speed of 4.8 m/s?

Expert Solution

(a)

As the engine approaches the shore, the wavelength of sound should decreases and hence frequency of sound increases. As frequency reflects the pitch of the sound, the engine sound higher piched as comapred to a person experienced on the boat.

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(b) Frequency, f = velocity / wavelength = ( 12.5 m/s ) / 100 m = 0.125 Hz

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(c)

As it headed away from the shore, the apperent frequency of sound:

f ( observed ) = ( 1 - v₀/ v ) f

= ( 1 - 4.8 / 343 ) ( 0.125 Hz )

= 0.123 Hz

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(d)

As it headed toward the shore, the apperent frequency of sound:

f ( observed ) = ( 1 + v₀/ v ) f

= ( 1 + 4.8 / 343 ) ( 0.125 Hz )

= 0.127 Hz

= 0.130 Hz ( almost equal to )

genius_generous answered 7 months ago

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