Question

If two waves both have frequencies of 800 Hz, can they produce beats? If you answer ‘yes", determine their beat frequency. If you answer ‘no', explain why they cannot produce beats. (b) If waves of frequencies 900 Hz and 902 Hz interfere, determine the beat period of the wave that they produce.

Answer 1

Two waves with the same frequency of 800 Hz cannot produce beats because they do not have any frequency difference. For waves with frequencies of 900 Hz and 902 Hz, the beat frequency is 2 Hz, which makes the beat period 0.5 seconds.

Step-by-step explanation:

If two waves both have frequencies of 800 Hz, they cannot produce beats because beats occur when there are two sound waves of different frequencies that interfere with each other. Since both waves have the same frequency, there is no difference in frequency to create the fluctuation in amplitude observed as beats.

For waves of frequencies 900 Hz and 902 Hz, the beat frequency would be the absolute difference between the two. The beat frequency would be 902 Hz - 900 Hz = 2 Hz. To determine the beat period, which is the inverse of the beat frequency, we use the formula T = 1/fB, where T is the beat period and fB is the beat frequency. Therefore, T = 1/2 Hz = 0.5 seconds.

Answer 2

(a) No , we will not hear any beat frequency

(b) The beat period of the wave that they produce is 2.0 Hz

Step-by-step explanation:

(a) No , we will not hear any beat frequency

Explanation

Beats occur when two waves of nearby frequencies overlap and create a new resultant wave for which maxima and minima amplitude of resultant wave varies at a particular position is space with time . The number of beats per second equals the difference in frequency between the two interfering waves .

If the beats occur more often than roughly 20 or 30 times per second, we no longer hear them as beats. Our ears are not fast enough to respond to events happening quickly. So for beats to occur there must be some difference between the interfering frequencies .

(b) Since the number of beats per second equals the difference in frequency between the two interfering waves.

`f_(beat)=\left | f_1-f_2 \right |`

=>
`f_(beat)=\left | 902-900 \right |\, Hz=2.0\, Hz`

Thus the beat period of the wave that they produce is 2.0 Hz