Question

You watch a distant lady driving nails into her front porch at a regular rate of 1 stroke per second. You hear the sound of the blows exactly synchronized with the blows you see. And then you hear one more blow after you see her stop hammering. How far away is she? The speed of sound is 340 m/s. a) 270 m. b) 680 m. c) 85 m. d) 1360 m. e) 170 m.

Answer 1

λ = 1360 m

Step-by-step explanation:

Given data:

frequency of driving nails is given as 1 stroke per second mean at every 0.25 sec she hit the nails

speed of sound is given as 340 m/s

we know that the wave equation is given as

Speed = frequency × wavelength,

v = f × λ

where,

v = speed in meters/second (m/s)

f = frequency in Hertz (Hz)

substituing value to get wavelength of her driving nails

`340 m/s = (1Hz)*  \lambda`

`\lambda = (340)/(0.25)`

λ = 1360 m

Answer 2

The distance of the lady is 340 m

Solution:

As per the question:

Regular rate of stroke = 1 stroke per second

Speed of sound, v = 340 m/s

Now,

To calculate the distance of the lady, we need to calculate the wavelength of the sound wave which provides the distance.

Now, we know that:

`v = \\u* \lambda`

where

`\\u` = frequency in Hz

`\lambda` = wavelength in meter

Also, we know that 1 stroke per second makes a frequency of 1 Hz

Thus

`340 = 1* \lambda`

`\lambda = 340\ m`