Question

What has the greatest effect on the speed of sound in air? a) temperature of the air b) frequency of the sound c) wavelength of the sound d) pressure of the atmosphere

Short answer

a) Temperature of the air b) Frequency of the sound wave c) Wavelength of the sound wave d) Atmospheric pressure Answer: a) Temperature of the air

Step-by-step solution

Recall the formula for the speed of sound in air

The formula for the speed of sound in air is given by: v = 331.3 m/s * sqrt(1 + T/273.15) where v is the speed of sound, T is the temperature in Celsius, and the 331.3 and 273.15 are constants derived from experimental data. From this formula, we can analyze the factors listed in the exercise.

Analyze temperature's effect on the speed of sound

In the formula for speed of sound, we can see that temperature is directly involved in the equation. As the temperature increases, the value inside the square root also increases, leading to a higher speed of sound.

Analyze frequency's effect on the speed of sound

Frequency is not included in the formula for the determination of the speed of sound and is not a direct factor in determining the speed of sound.

Analyze wavelength's effect on the speed of sound

Wavelength is also not included in the formula for the determination of the speed of sound and is not a direct factor in determining the speed of sound.

Analyze atmospheric pressure's effect on the speed of sound

Atmospheric pressure has a negligible impact on the speed of sound in air. The speed of sound is primarily determined by the temperature and medium, while pressure has a much smaller effect.

Conclusion

Based on the analysis, option a) temperature of the air has the greatest effect on the speed of sound in air. The other factors, frequency, wavelength, and atmospheric pressure have less direct impact on the speed or are not directly involved in determining the speed of sound in air.

Key concepts

Temperature's Effect on Speed of Sound

Understanding how temperature affects the speed of sound in air is essential when studying wave phenomena. As temperature rises, the air molecules move more vigorously due to increased thermal energy. This energized movement results in particles colliding more frequently, allowing sound waves to travel faster through the medium.

The mathematical relationship, as seen in the formula provided in the problem solution (\(v = 331.3 \text{ m/s} \times \text{sqrt}(1 + T/273.15)\)), illustrates that the speed of sound (\(v\)) increases as the square root of the sum of one and the ratio of the air temperature (\(T\)) in Celsius to the constant 273.15. This direct correlation signifies that an increase in temperature will always result in an increase in the speed of sound, which is why variation in temperature plays such a pivotal role compared to other factors.

Frequency's Effect on Sound Speed

Frequency, defined as the number of times per second that a sound wave cycles, is a fundamental aspect of sound. However, it's important to clarify that frequency does not affect the speed of sound in air. The speed of a sound wave is determined by the medium through which it travels and the conditions of that medium, such as temperature.

This means that whether you hear a high-pitched whistle or a low rumble of thunder, the speed at which those sounds reach your ears depends solely on the air conditions, not the frequency of the sound waves. Given that frequency and speed of sound are unrelated, it helps us to understand why a soprano's high note and a bass's low note, sung simultaneously, travel through the opera house at the same speed.

Wavelength's Impact on Sound Speed

Wavelength is another characteristic of sound waves that some may expect to influence the speed of sound, but this is not the case. Wavelength is the distance between successive crests of a wave, which at a fixed speed, inversely varies with frequency. It's vital to understand that the wavelength of sound changes only if the frequency changes while the speed of sound remains constant.

As the formula for speed of sound does not include wavelength, and since we have discussed that frequency doesn't affect speed, it is clear that the wavelength has no direct impact on the speed of sound in air. This can be somewhat counterintuitive, as in many scenarios, distance-related measures do impact velocity, but for sound in air, this relationship does not apply.

Atmospheric Pressure's Impact on Sound Speed

Lastly, atmospheric pressure, which is the weight of the air above us, might seem like it would have a considerable effect on the speed of sound. After all, pressure influences many gas behaviors. However, for sound speed in air, the impact of atmospheric pressure is indeed minimal.

Sound is a mechanical wave, and while it requires a medium to travel, its speed is not significantly affected by changes in pressure. This is because, at a constant temperature, the density and pressure of the air change proportionally, leaving the speed of sound largely unchanged. Therefore, in typical atmospheric conditions, whether you're at sea level or on a mountain, the variation in sound speed due to pressure differences is not pronounced. This is why atmospheric pressure is not the primary factor affecting the speed of sound, and the temperature reigns supreme in this domain.