Waves equation problems

Question

1.Dog whistles are inaudible to humans because dogs can hear at much higher frequencies than humans are capable of detecting. If a dog whistle has a wavelength of 3.5 x 10^-3 m, what is the frequency of sound emitted? *Sound travels at 340 m/s.

2.What is the speed of sound in air that has a temperature of -6.9  ^o C?

3.What is the wavelength of sound in air that has a temperature of -16.5  ^o C has a frequency of 30 Hz?

*answer and explanation please*

Answer 1

Ques 1: Easy to obtain using relationship v = λ.f

Ques 2: Speed of sound in an ideal gas is related as

v = SQRT (γRT/M),

where γ is the adiabatic constant (a property of the gas)

R is the Universal Gas Constant, 8.314 J/mol K

T is the temperature (ºK)

M is the molecular mass of the gas (Kg/Mol)

For air,

γ = 1.4

Avg Molecular Weight, M = 28.95 g/mol

Ques 3: Use equations for velocity of sound in questions 1 and 2 to find the answer.