Question

A trombone plays a note that is 501 Hz. The wavelength of the sound is 1.10 m. What is the air temperature in degrees Celsius??

Answer 1

To solve this problem, we can use the formula:

wavelength = (speed of sound) / frequency

We can rearrange this formula to solve for the speed of sound:

speed of sound = wavelength x frequency

The speed of sound depends on the air temperature, so we can use this formula to find the temperature:

speed of sound = 331.3 + 0.606 x temperature (in degrees Celsius)

Substituting the given values:

1.10 = (331.3 + 0.606 x temperature) / 501

Multiplying both sides by 501:

551.1 = 331.3 + 0.606 x temperature

Subtracting 331.3 from both sides:

219.8 = 0.606 x temperature

Dividing both sides by 0.606:

363.0 = temperature

Therefore, the air temperature is approximately 363.0 degrees Celsius.

Answer 2

The speed of sound in air can be calculated using the formula:

v = fλ

where v is the speed of sound, f is the frequency, and λ is the wavelength.

Substituting the given values, we have:

v = (501 Hz) (1.10 m)

v ≈ 551 m/s

The speed of sound in air depends on the temperature of the air. The relationship between the speed of sound (v) and the temperature (T) is given by:

v = 331.4 + 0.6T

where v is in m/s and T is in degrees Celsius.

Solving for T, we have:

T = (v - 331.4) / 0.6

Substituting the value of v that we calculated earlier, we get:

T = (551 - 331.4) / 0.6

T ≈ 365 Celsius

Therefore, the air temperature is approximately 365 degrees Celsius. However, this result is much higher than the maximum possible temperature for air, which is around 2000 Kelvin (about 1727 Celsius). This suggests that there may be an error in the given values or in the calculation.

I Hope This Helps!