Question

A source X of unknown frequency produces 8 beats per second with a source of 250 Hz and 12 beats per second with a source of 270 Hz. The frequency of the source X is(a) 242 Hz(b) 258 Hz(c) 282 Hz(d) 262 Hz

Answer 1

The unknown frequency X is given by  = Frequency ± number of beats

In the first case -

A source X of unknown frequency produces 8 beats per second with a source of 250 Hz .

Here, number of beats per second = 8

=>  The frequency of the source X = 250 ± 8

                                                        =  258 Hz  or  242  Hz

In the second case -

A source X of unknown frequency produces 12 beats per second with a source of 270 Hz .

Here, number of beats per second = 12

=>  The frequency of the source X = 270 ± 12

                                                        =  282 Hz  or  258  Hz

Thus, in both cases the common value of unknown frequency of source X is 258 Hz .

Thus, the frequency of the source X is 258 Hz .

So, option  (b) 258 Hz  is correct .

Answer 2

Answer:

B) 258hz

Explanation:

Since the source of frequency x gives 8 beats per second with frequency 250 Hz, it's possible frequency are 258 or 242.

As the source of frequency x gives 12 beats per second with a frequency 270 Hz, it's possible frequencies 282 or 258 Hz.

The frequency of source S = 270 ± 12

                                            = 282 or 258

If S have frequency of 258 Hz then it will given 8 beats/s  Thus, S will have the frequency of 258 Hz.