Question

What is the carrier frequency in an AM wave when its highest frequency component is $850Hz$ and the bandwidth of the signal is $50Hz$ ?
A. $85Hz$
B. $825Hz$
C. $25Hz$
D. None of these

Answer 1

In order to solve this question, firstly we should know that bandwidth is the difference between upper band frequency and lower band frequency so, by using this concept we will find out the value of lower band frequency and then using the general formula of carrier wave frequency we will find the correct option belonging to carrier wave frequency.

Complete step by step answer:
According to the question, we have given that upper band frequency as $Upper{\kern 1pt} f = 850Hz$
Bandwidth as $Bandwidth = 50Hz$ now using the concept that,
Bandwidth is equal to upper band frequency minus lower band frequency as
$bandwidth = Upper{\kern 1pt} f - lower{\kern 1pt} f$
on putting the values we get,
$50 = 850 - lower{\kern 1pt} f$ so we get,
$lower{\kern 1pt} f = 850 - 50$
$lower{\kern 1pt} f = 800Hz$

So, we have now lower band frequency of $lower{\kern 1pt} f = 800Hz$
and as we know that, carrier wave frequency can be written as
$F = lower{\kern 1pt} f + \dfrac{{(bandwidth)}}{2}$ where F denotes for carrier wave frequency so, on putting the values of each parameter we get,
$F = 800 + \dfrac{{(50)}}{2}$
on further solving for F we get,
$F = 800 + 25$
$\therefore F = 825Hz$
so, we find that is the carrier frequency in an AM wave when its highest frequency component is $850Hz$ and the bandwidth of the signal is $50Hz$ is $F = 825Hz$

Hence, the correct option is B.

Note: It should be remembered that, AM stands for amplitude modulation, which is a process of modulating the waves by changing their amplitudes and is widely used in electronics and communication fields for example radio carrier waves are such an example of amplitude modulation.