Question

A sound wave with a pitch of 261.6Hz (middle C) is played in a warm concert hall, where the air temperature is 25​∘​​C. A passer-by in the cold winter street outside hears the note coming through a window. The air temperature outside is -5​∘​​C.

a.) What will be the frequency of the sound heard outside in the cold air? Give an answer accurate to one decimal point. (Hz)

b.)What will be the wavelength of the sound wave in the warm concert hall? Give an answer accurate to at least 2 decimal points. (m)

c.) What will be the wavelength of the sound wave outside in the cold air? Give an answer accurate to at least 2 decimal points. (m)

Answer 1

Frequency of sound does not change. Hence frequency of sound heard outside is 261.6 Hz

b) wave length = speed of sound / frequency

Speed of sound at normal temperature of 25 deg C ( 298 K) = 345 m/s. Hence wave length inside the hall

= 345 / 261.6 = 1.32 m

c) Speed pf sohnd and wave length are directly proportional to root of temperature in Kelvin. Hence wavelength ,outside

= wavelength inside √ (outside temperature/inside temperature)

= 1.32√(268/298) = 1.25 m