Question

help me please in solving this question of physics​

Answer 1

Answer:

Question :

Wavelength of 2 waves are in 85/170 m and 85/172 m .These waves produces 4 beats with a 3rd node of fixed frequency n. Find the frequency of 3rd node and velocity of the waves.

Given:

The supplied wavelengths are :

• 85/170 m
• 85/172 m

3rd node has frequency of "n"

To find:

Frequency of 3rd node and velocity of wave.

Concept:

Let Frequency of the way be f1 and f2.

$\therefore \: f1 = \dfrac{v}{ (\frac{85}{170}) } \\ \\ = > f1 = \dfrac{170v}{85}$

$\therefore \: f2 = \dfrac{v}{( \frac{85}{172}) } \\ \\ = > f2 = \dfrac{172v}{85}$

Since both these frequencies produce 4 beats , so we can say that :

• f2 - n = 4 .....(1)
• n - f1 = 4 .....(2)

Calculation:

If we add eq(1) and eq(2) , then

$\therefore \: f2 - f1 = 8$

$= > \dfrac{172v}{85} - \dfrac{170v}{85} = 8 \\ = > \dfrac{2v}{85} = 8 \\ = > v = 85 \times 4 \\ = > v = 340 \: m {s}^{ - 1}$

So putting value of "v" in f2

$f2 = \dfrac{172v}{85} \\ = > f2 = \dfrac{172 \times 340}{85} \\ = > f2 = 172 \times 4 = 688 \: hz$

Now putting f2 in eq(1)

$f2 - n = 4 \\ = > 688 - n = 4 \\ = > n = 684 \: hz$

So final answer :

$\boxed{velocity = 340 \: m {s}^{ - 1}} \\ \boxed{n = 684 \: hz}$