Question 75: Waves

Question

Two travelling waves produces a standing wave represented by equation,
y = 1.0 mm cos(1.57 cm
$$-$$1
) x sin(78.5 s
$$-$$1
)t.
The node closest to the origin in the region x > 0 will be at x = .............. cm.

Accepted Answer

For node
cos(1.57 cm
$$-$$1
)x = 0
(1.57 cm
$$-$$1
)x = $${\pi  \over 2}$$
x = $${\pi  \over {2(1.57)}}$$ cm = 1 cm

Waves

Two travelling waves produces a standing wave represented by equation, y = 1.0 mm cos(1.57 cm $-1 ) x sin(78.5 s -$1 )t. The node closest to the origin in the region x > 0 will be at x = .............. cm.

Integer / Numeric Answer Type