the frequency of middle C on a piano is 261.6hz. What is the wavelength of sound as it travels @room air and in water?

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To calculate the wavelength of sound, we can use the formula:

wavelength = speed of sound / frequency

The speed of sound is approximately 343 meters per second in room air and approximately 1,484 meters per second in water.

1) Wavelength in room air:
wavelength = speed of sound in room air / frequency

Given:
Frequency (f) = 261.6 Hz
Speed of sound in room air = 343 m/s

Using the formula:
wavelength (in room air) = 343 m/s / 261.6 Hz

Calculating:
wavelength (in room air) ≈ 1.3126 meters or 131.26 centimeters

2) Wavelength in water:
wavelength = speed of sound in water / frequency

Given:
Frequency (f) = 261.6 Hz
Speed of sound in water = 1,484 m/s

Using the formula:
wavelength (in water) = 1,484 m/s / 261.6 Hz

Calculating:
wavelength (in water) ≈ 5.667 meters or 566.7 centimeters

Therefore, the wavelength of middle C on a piano is approximately 1.3126 meters in room air and approximately 5.667 meters in water.

To find the wavelength of sound in air and water, we can use the formula:

wavelength = speed of sound / frequency

The speed of sound in air is approximately 343 meters per second at room temperature and pressure. In water, sound travels faster, at around 1,482 meters per second.

Let's calculate the wavelength for middle C in air:

wavelength = speed of sound / frequency
wavelength = 343 m/s / 261.6 Hz

Calculating this, we find that the wavelength of middle C in air is approximately 1.31 meters.

Now let's calculate the wavelength for middle C in water:

wavelength = speed of sound / frequency
wavelength = 1482 m/s / 261.6 Hz

Calculating this, we find that the wavelength of middle C in water is approximately 5.66 meters.

So, the wavelength of sound as it travels in air is about 1.31 meters, and in water, it is about 5.66 meters.

λ= v/f

air 20°C : v1 =343 m/s
water : v2= 1500 m/s