Physics Question? Waves and Sound?

Question

Part 1/2

The range of human hearing extends from

approximately 20 Hz to 20000 Hz. Find the wavelength for 47.5 Hz at a temperature

of 30.3 ◦C. Assume the velocity of

sound at 0◦C is 331 m/s. Answer in units of m. ANSWER= 7.35 m

Part 2/2

Find the wavelength for 1040 Hz at a temperature of 30.3 ◦C. Answer in units of cm. ????????? Please help

Answer 1

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It depends which method you are meant to use to find speed. Different methods give slightly different answers (some are more accurate than others).

Here are 2 ways:

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Method 1: the speed is proportional to the absolute temperature:

0°C = 273.15K

30.3° = 273.15 + 30.3 = 303.45K

Using proportionality: v = 331 x √(303.45/273.15) = 348.88m/s

v = λf

λ = v/f = 348.88/47.5 = 7.34m (close to your required answer)

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Method 2. Use the fact that the speed of sound increases by approximately 0.6m/s for each 1°C temperature rise:

Temperature rise = 30.3 - 0 = 30.2°C

New speed = 331 + 30.2x0.6 = 349.12m/s

λ = v/f = 349.12/47.5 = 7.35m (same as your required answer)

So I guess the second method is the one they want.

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For part b), the temperature and speeds are the seams as part a) so:

λ = v/f = 349.12/1040 = 0.336m = 33.6cm

Answer 2

dont know