1) Transverse waves travel with a speed of 25.0 m/s on a string under a tension

Question

1) Transverse waves travel with a speed of 25.0 m/s on a string under a tension of 6.30 N. What tension is required for a wave speed of 29.0 m/s on the same string?

2) A driver travels northbound on a highway at a speed of 24.0 m/s. A police car, traveling southbound at a speed of 41.0 m/s, approaches with its siren producing sound at a frequency of 2600 Hz.

(a) What frequency does the driver observe as the police car approaches?
Hz

(b) What frequency does the driver detect after the police car passes him?
Hz

(c) Repeat parts (a) and (b) for the case when the police car is traveling northbound.

Explanation / Answer

1.

V = sqrt(T / µ)
25 = sqrt(6.30 / µ)
µ = 0.01008

29 = sqrt(T/µ)
841 = T/µ
T = µ x 841
BUT
µ = 0.01008
Therefore,
T = 0.01008 x 841
T = 8.477 N

2.

Assuming temperature is 20*C and speed of sound in the air is 343 m/s:

f' = f * (343 +/- vo) / (343 -/+ vs )

When deciding whether to use + or -, just think about it logically. If the observer is moving opposite the directions of the waves, then the observer will run into more waves, making the frequency higher, so use + for vo. If the observer is in the trail the source (in other words, behind the source), then the observer will run into fewer waves, so use + for vs.

a) f' = 2600 * (343 + 24) / (343 - 41) = 3159.60 Hz

b) f' = 2600 * (343 - 24) / (343 + 41) = 2159.90 Hz


If the source is traveling northbound:

a) f' = 2600 * (343 - 24) / (343 - 41) = 2746.36 Hz

b) f' = 2600 * (343 + 24) / (343 + 41) = 2484.90 Hz

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