A sound wave is emitted at a frequency of 300 Hz in air at a 0°C. As the sound wave travels through the air, the temperature increases. What is the wavelength of the sound wave at the following temperatures?
a. 0°C
b. 20°C
c. 45°C

• A. (a) λ=1.10 m; (b) λ=1.14 m; (c) 1.19 m
• B. (a) λ=1.10 m; (b) λ=1.14 m; (c) 1.29 m
• C. (a) λ=1.10 m; (b) λ=1.18 m; (c) 1.19 m
• D. (a) λ=1.10 m; (b) λ=1.18 m; (c) 1.29 m

Answer: (A)

Verified step by step guidance

1. Understand that the speed of sound in air is affected by temperature. The speed of sound at 0°C is approximately 331.5 m/s. The speed increases by about 0.6 m/s for each degree Celsius increase in temperature.
2. Use the formula for the speed of sound in air as a function of temperature: v = 331.5 + 0.6 * T, where T is the temperature in degrees Celsius.
3. Calculate the speed of sound at each given temperature using the formula. For example, at 20°C, substitute T = 20 into the formula to find the speed of sound.
4. Use the relationship between speed, frequency, and wavelength: v = f * λ, where v is the speed of sound, f is the frequency, and λ is the wavelength. Rearrange the formula to solve for wavelength: λ = v / f.
5. Substitute the calculated speed of sound and the given frequency (300 Hz) into the formula to find the wavelength at each temperature. Repeat this process for each temperature: 0°C, 20°C, and 45°C.