A string vibrates with frequency 500 Hz; another string nearby vibrates at 504 H

Question

A string vibrates with frequency 500 Hz; another string nearby vibrates at 504 Hz. Find the following:

(a )The beat frequency

(b) The other frequency heard, in addition to the beat frequency

Please use the following equations because I will be expected to use them as well. Also, please show me the steps that you used (in legible writing) to solve for the answer. Thank You.

(a) for finding the beat frequency, use the equation: F(beat) = |F(1) - F(2)|

Attached below is an image of the equation I was told to use to solve the above problem. This is (18.10)

one hear a periodi Definition beating of enon is called beating- point due to the wrating is the periodic varution in amplirsele at frequencies. superpoution of waves having slightly different The number of ampliande maxima one hears per as we shall sho below. equals the dillerence frequency the theo sources about 20 beatss. mum beat frequency that the human ear can detect with when the beat frequency exceeds this value, the beats blend indistinguishably the sound them. amplitude and slightly different frequencies equal similar to Equation 16.13 to and traveling through a medium. We use equations identify as 0. the wave functions for these two es at a point that we We also choose the phase angle in Equation 1613 asis m/2 A cos (2m/h) Acos (2 fri) sing the superposition principle, we find that the resultant wave function at this The trigonometric identity allows us to write the expression for yas (18.10) Resultant of two waves of different frequencies but equal amplitude Graphs of the individual waves and the resultant wave are shown in Figure 18.17. From the factors in Equation 18.10, we see that the resultant wave has an effective Figure 18.17 Beata are dightly fillerew frequen The individual waves

Explanation / Answer

(A)

For beat frequrency = 504 -500

= 4 beats per second

(b)

The other frequency that can be heard is (f1 +f2)/2 form eqn 18.10

= 500+504/2

= 502 Hz

=

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