How Do You Calculate the Frequency of Microwaves Using Standing Waves?

[Amith2006]

Sir,
1)Microwaves are directed normally at a plane metallic reflector. A detector moving along the normal to the reflector travels 15 cm from the first to the 11th successive of minimum intensity. What is the frequency of the microwave?(velocity of microwaves = 3 x 10^8 m/sec)
I solved it in the following way:
The incident and the reflected microwaves superimpose to produce standing waves. The distance between the first and the 11th minimum is given that it is 15 cm.
Therefore,
0.15 = 10 x (lambda/2)
Lambda = 0.03 meters
Frequency = (3 x 10^8)/ 0.03
= 10^10 Hz
Is it right?
2)Two waves of same frequency travel in opposite directions in a medium with amplitudes 3 units and 2 units respectively. What is the ratio of the amplitudes at an antinode and a node in the stationary wave?
I think it is infinity because at the antinode it has maximum amplitude and at the node it is zero. Is it right?

 

[Hootenanny]

Sir,
1)Microwaves are directed normally at a plane metallic reflector. A detector moving along the normal to the reflector travels 15 cm from the first to the 11th successive of minimum intensity. What is the frequency of the microwave?(velocity of microwaves = 3 x 10^8 m/sec)
I solved it in the following way:
The incident and the reflected microwaves superimpose to produce standing waves. The distance between the first and the 11th minimum is given that it is 15 cm.
Therefore,
0.15 = 10 x (lambda/2)
Lambda = 0.03 meters
Frequency = (3 x 10^8)/ 0.03
= 10^10 Hz
Is it right?

This looks good to me. Just a small point however, using standard scientific notation it is better to quote the answer as 1x10¹⁰ Hz. However, both are correct.

2)Two waves of same frequency travel in opposite directions in a medium with amplitudes 3 units and 2 units respectively. What is the ratio of the amplitudes at an antinode and a node in the stationary wave?
I think it is infinity because at the antinode it has maximum amplitude and at the node it is zero. Is it right?

Are you sure about that? The formal definition of a node is "a point of minimum displacement.", this need not to be zero. The important thing to note is the respective amplitudes, try sketching the two waves in anti-phase on the same graph.

~H

 

[kyle8921]

1) Yes, your calculation for the frequency of the microwave is correct. The frequency of the microwave in this scenario is 10^10 Hz.

2) Yes, you are correct. The ratio of amplitudes at an antinode and a node in a stationary wave is infinity, as the amplitude at the antinode is at its maximum while the amplitude at the node is zero.