Question

One day when the speed of sound in air is 343 m/s, a fire truck traveling at vs = 34 m/s has a siren which produces a frequency of fs = 449 Hz. Randomized Variables vS = 34 m/s f = 449 Hz show answer No Attempt 50% Part (a) What frequency (in Hertz) does the driver of the truck hear? fd = | sin() cos() tan() cotan() asin() acos() atan() acotan() sinh() cosh() tanh() cotanh() Degrees Radians π ( ) 7 8 9 HOME E ↑^ ^↓ 4 5 6 ← / * 1 2 3 → + - 0 . END √() BACKSPACE DEL CLEAR Grade Summary Deductions 0% Potential 100% Submissions Attempts remaining: 3 (4% per attempt) detailed view Hints: 4% deduction per hint. Hints remaining: 1 Feedback: 5% deduction per feedback. No Attempt No Attempt 50% Part (b) What frequency (in Hertz) does an observer hear when the truck is moving away?

Answer 1

Answer:

a) 449 Hz b) 409 Hz

Explanation:

a)

• As the driver is moving at v=0 related to the truck, he hears the same frequency that the siren is producing, i.e., 449 Hz.

b)

• For  the observer at rest, the frequency that he hears, is modified due to the truck is moving away from him at v= 34 m/s, so the Doppler Effect is present.
• The Doppler Effect says that the perceived frequency f' is related with the actual frequency f by the following equation:$f_{obs} = f_{source} *(\frac{v_{sound}}{v_{sound}+v_{source} }) =\\ \\ 449 Hz * (\frac{343 m/s}{377 m/s} = 409 Hz$

Answer 2

(a) The frequency will be "449 Hz".

(b) Frequency heard be observer will be"408.5 Hz".

Given:

Speed of sound,

• $V = 343 \ m/s$

Speed of truck,

• $V_s = 34 \ m/s$

Frequency of siren,

• $f_s = 449 \ Hz$

(a)

→ Frequency of sound heard by truck driver = Frequency of siren

Thus,

→ $f_d = 449 \ Hz$

(b)

The frequency heard by the observer will be:

→ $f_o = (\frac{V}{V+V_s} )f_s$

By substituting the values, we get

→     $= (\frac{343}{343+34} )\times 449$

→     $=0.909\times 449$

→     $=408.5 \ Hz$

Thus the above answers are correct.  

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