Question

When the air temperature increases, the wave-length of the sound from the tuning fork (1) increases (2) remains the same, or (3) decreases. Why? If the temperature rises from 0 degrees C to 20 degrees C, what is the change in wavelength?

Answer 1

When the air temperature increases, the wave-length of the sound from the tuning fork - (1) increases

We know that,

wavelength = v / f

frequency remains same with temperature change. so, wavelength depends on speed of sound.

v = 331 + 0.6*T

When temperature is increased, speed of sound increases. hence, wavelength increases.

At 0 deg,

v = 331 + 0.6*0 = 331 m/s

= 331 / f

at 20 deg,

v = 331 + 0.6*20 = 343 m/s

= 343 / f

change in wavelength, delta = (343 - 331) / f

= 12 / f

Answer 2

When the air temperature increases, the wavelength of the sound from the tuning fork increases. Here's why:

1. Speed of Sound and Temperature: The speed of sound in air increases as the temperature rises. This happens because warmer air molecules move faster, allowing sound waves to travel more quickly.

• The formula for the speed of sound in air is:

  $$v\approx 331\text{m/s}+(0.6\times T\text{°C})$$

  where $T$ is the temperature in Celsius.

• 
  

2. Frequency Remains Constant: The frequency of the tuning fork's sound doesn't change because it depends only on the fork's physical properties (like its shape and material), not the surrounding air.

3. 
   

4. Wavelength and Speed: Since the speed of sound ($v$) increases and the frequency ($f$) stays the same, the wavelength ($\lambda$) must also increase (because $\lambda =\frac{v}{f}$).

5. 
   

Calculation for 0°C to 20°C:

• At 0°C:

  $$v_0=331+(0.6\times 0)=331\text{m/s}$$

• At 20°C:

  $$v_{20}=331+(0.6\times 20)=343\text{m/s}$$

• The wavelength ratio is proportional to the speed ratio (since frequency is constant):

  $$\frac{{\lambda }_{20}}{{\lambda }_0}=\frac{v_{20}}{v_0}=\frac{343}{331}\approx 1.036$$

  So, the wavelength increases by about 3.6% when the temperature rises from 0°C to 20°C.

• 
  

 Warmer air = faster sound = longer wavelength for the same tuning fork note