Question

Wind instruments usually warm up from the player’s breath. Calculate the maximum change expected if the instrument is tuned to concert A (440 Hz) at the room temperature of 23oC and then warmed up to body temperature of 37.0oC.

Answer 1

Answer: 7.7Hz

Step-by-step explanation:

The frequency of a sound wave produced by a wind instrument depends on the speed of sound in the medium, which in turn depends on the temperature of the medium. The speed of sound in air at room temperature (23°C) is approximately 343 meters per second. At body temperature (37.0°C), the speed of sound in air is approximately 349 meters per second.

To calculate the expected maximum change in frequency of a wind instrument when warmed up from room temperature to body temperature, we can use the following formula:

Δf/f = Δv/v,

where Δf is the change in frequency, f is the initial frequency (in Hz), Δv is the change in speed of sound, and v is the initial speed of sound (in meters per second).

Substituting the values, we get:

Δf/440 = (349 - 343)/343

Δf/440 = 6/343

Δf = (6/343) × 440

Δf ≈ 7.7 Hz