Question

The first resonant length of an open air column in resonance with a 512 Hz fork is 33. 0 cm. Find the speed of sound.

Answer 1

The speed of sound in open air can be calculated using the formula: Speed of sound = Frequency x Wavelength. By using the formula for the first resonant length of an open air column, we can find the speed of sound based on the given values of the frequency and length.

Step-by-step explanation:

To find the speed of sound, we can use the formula: Speed of sound = Frequency x Wavelength. The fundamental frequency of the open air column is 512 Hz, and the first resonant length is 33.0 cm. We can use the formula for the first resonant length of an open air column, which is given by: L = (2n - 1) * (v/4f), where L is the length, n is the harmonic number, v is the velocity of sound, and f is the frequency. For the first resonant length, n = 1. Plugging in the given values, we can solve for v: 33.0 cm = (2 * 1 - 1) * (v/4 * 512 Hz). Rearranging the equation, we get: v = 4 * 512 Hz * 33.0 cm / (2 * 1 - 1) = 66,048 cm/s. Therefore, the speed of sound is 66,048 cm/s.

Answer 2

Given that the length of the open-air column is L = 33 cm = 0.33 m

The frequency of the air column is f = 512 Hz

We have to find the speed of sound, v.

The speed of sound can be calculated by the formula,

`\begin{gathered} f=(v)/(2L) \\ v=2L* f \end{gathered}`

Substituting the values, the speed of sound will be

`\begin{gathered} v=2*0.33*512 \\ =337.92\text{ m/s} \end{gathered}`

Thus, the speed of sound is 337.92 m/s.