Question

Wind instruments like trumpets and saxophones work on the same principle as the "tube closed on one end" that we examined in our last experiment. What effect would it have on the pitch of a saxophone if you take it from inside your house (at 76 degrees F) to the outside on a cold day when the outside temperature is 45 degrees F ?

Answer 1

f = v / 4L

the frequency of the instruments is reduced by the decrease in the speed of the wave with the temperature.

Step-by-step explanation:

In wind instruments the wave speed must meet

v = λ f

λ = v / f

from v is the speed of sound that depends on the temperature

v = v₀
`\sqrt{1+ (T [C])/(273) }`

where I saw the speed of sound at 0ºC v₀ = 331 m/s the temperature is in degrees centigrade, we can take the degrees Fahrenheit to centigrade with the relation

(F -32) 5/9 = C

76ºF = 24.4ºC

45ºF = 7.2ºC

With this relationship we can see that the speed of sound is significantly reduced when leaving the house to the outside

at T₁ = 24ºC v₁ = 342.9 m / s

at T₂ = 7ºC v₂ = 339.7 m / s

To satisfy this speed the wavelength of the sound must be reduced, so the resonant frequencies change

λ / 4 = L

λ= 4L

v / f = 4L

f = v / 4L

Therefore, the frequency of the instruments is reduced by the decrease in the speed of the wave with the temperature.