Question

1) What is the speed of sound waves in Antarctica if the temperature is -40.0°C? ____m/s

2) A certain musical instrument's string is 0.40 m long and has a μ = 0.002 kg/m. It is tuned to a fundamental frequency of 590 Hz. Calculate the tension in the string. _____N

3)The 6th harmonic of standing waves in a string of length L has a wavelength of 0.4417 m, while the 5th harmonic has a wavelength of 0.5300 m. Find L, the length of the string. _____m

Answer 1

1)

speed of sound changes as v = 331+ (0.6*t)

v = 331 - (0.6*40)

v = 307 m/s

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2)

fundamental frequency f = v/(2L)

v = speed of sound = 2L*f

but speed in a string v = sqrt(T/mue)

2*L*f = sqrt(T/mue)

2*0.4*590 = sqrt(T/0.002)

T = 445.5 N

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3)

total length of wire L = n*lambda/2

wavelength lambda = 2L/n

for 6 th harmonic

0.4417 = 2*L/6

L = 1.3251 m <<<---answer