Question

The speed of sound is proportional to the square root of the absolute temperature, defined by:

Tabs = 273 + Tc

where Tc is the temperature in degrees Celsius. A trumpet is tuned to B♭ (466 Hz), when it is initially cold at 20◦C. After playing for a while, it warms up to 30◦C. What is the new frequency of the trumpet (i.e., how far out of tune is it)? Assume the speed of sound at 20◦C to be 343 m/s, and that the trumpet (and therefore the wavelength) does not change.

To get started: calculate the speed of sound at the higher temperature, given that you know what it is at the lower temperature. Then if the speed of sound changes, how do frequency and wavelength change? Is one of them held fixed by the design of the trumpet?

Answer 1

Speed of sound,

v

v = k

k = 343 / = 20.038

Speed of sound at 30 oC, v' = 20.038 *

v' = 348.8 m/s

We know that, v = f

= 343 / 466 = 0.736 m

New frequency,

f' = v' /

f' = 348.8 / 0.736

f' = 473.8 Hz