Question

An ultrasonic sound generator generates a wave of wavelength 1.6 cm and frequency 22 kHz.

ii. A plane uses this generator to measure the altitude. It receives the reflected signal 8 seconds later. The speed of the plane is 256 m/s. Find the approximate altitude of the plane.
(Assume that both the generator and receiver are very close to each other.)

(Use the value $\sqrt{57}$ ≈ 7.5)

[2 marks]

• A. 760 m
• B. 960 m
• C. 1,000 m
• D. 1,280 m

Answer 1

The correct option is B 960 m

Given,
Speed of plane = 256 m/s
Speed of sound = 352 m/s
Time taken = 8 seconds

The plane generates ultrasonic sound at point A and receives it at B.
The sound travels at ADB path, and the plane travels at ACB path.

In both cases, the time taken is 8 s.

ACB = Speed of plane $\times$ Time
= 256 $\times$ 8 m
ADB = Speed of sound $\times$Time
= 352 $\times$8 m

$AC=\frac{ACB}{2}=\frac{256\times 8}{2}m=256\times 4mAD=\frac{ADB}{2}=\frac{352\times 8}{2}m=352\times 4m$

$CD=\sqrt{A{D}^2-A{C}^2}=\sqrt{{(352\times 4)}^2-{(256\times 4)}^2}m=4\sqrt{{(32\times 11)}^2-{(32\times 8)}^2}m=32\times 4\sqrt{{\left(11\right)}^2-{\left(8\right)}^2}m=32\times 4\sqrt{121-64}m=128\sqrt{57}m=128\times 7.5m=960m$