Question

A clarinet, which is essentially a tube that is open at one end, is properly tuned to concert A (440 Hz) indoors, where the temperature is 20 ◦C and the speed of sound is 340 m/ s. A musician then takes the instrument to play an outdoor concert, where it is cold and the speed of sound is 333 m/ s. What is the frequency of the A played on the cold clarinet? (Ignore temperature related geometric changes in the body of the clarinet itself.)

A) 427 Hz
B) 431 Hz
C) 426 Hz
D) 435 Hz
E) 436 Hz

Answer 1

To find the frequency of the A played on the cold clarinet, we can use the formula f2 = (v2/v1) * f1, where f2 is the frequency of the A played on the cold clarinet, v2 is the speed of sound in the outdoor environment (333 m/s), v1 is the speed of sound in the indoor environment (340 m/s), and f1 is the original frequency of concert A (440 Hz). Using the given values, the frequency of the A played on the cold clarinet is 431 Hz.

Step-by-step explanation:

To find the frequency of the A played on the cold clarinet, we can use the formula:

f2 = (v2/v1) * f1

Where f2 is the frequency of the A played on the cold clarinet, v2 is the speed of sound in the outdoor environment (333 m/s), v1 is the speed of sound in the indoor environment (340 m/s), and f1 is the original frequency of concert A (440 Hz).

Plugging in the given values, we get:

f2 = (333/340) * 440 = 431 Hz

So the frequency of the A played on the cold clarinet is 431 Hz.