1. A 107.9 cm-long steel string with a linear density of 1.33 g/m is under 266.6

Question

1.

A 107.9 cm-long steel string with a linear density of 1.33 g/m is under 266.67 N tension. It is plucked and vibrates at its fundamental frequency.

What is the wavelength of the sound wave that reaches your ear in a 29.95oC room?

2. An air-track glider attached to a spring oscillates between the 20 cm mark and the 66 cm mark on the track. The glider completes 19.36 oscillations in 42.02 s. What is the period?

3. A guitar player, riding on a bus moving at 25 m/s, wishes to tune his guitar to a stationary source on the side of the road. If the source has a frequency of 440 Hz how many Hz would the guitar string (of length 0.6 m), be off, if tuned while the bus was moving, once the bus stops? Assume the speed of sound is 340 m/s.

Explanation / Answer

V^2 = T / (m/L) = 266.67 / ( 0.001 / 1.079 ) = 2.87*10^5

V = 536.41 m/s

? = 2m
f = 268.2 Hz

But what is the speed of sound in air at 29.95?C ? Guessing 343 m/s

Then
? (air ) = 343 / 268.2 = 1.2789 m

2.

19.36 oscillations in 42.02 s.
42.02 s for 19.36 oscillations.
42.02 / 19.36 second for one oscillation
Period of the oscillations = 42.02 /19.36 = 2.17 s.

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