Respuesta :
Answer:
69.6m
Explanation: Given that:
∆t = 0.19s
V.air = 347m/s
V.rod = 19×V.air
Also note that both sound covers the same distance both in two different medium.
Let us assume that x is the length of the rod, and the time it takes for sound in air to travel that distance is:
tₐ = x / 347
The time it takes for sound to travel through the rod is:
t = x / (19 × 347)
The difference between these is 0.19s:
tₐ - t = 0.19
x / 347 - x / (19 × 347) = 0.19
6593x-347x/2287771 = 0.19
6246x = 434676.49
x = 434676.49/6246
x = 69.59m
x = 69.6m
Answer:
The length of the rod is 69.6 m
Explanation:
From the question,
The speed of sound in the rod is 19 times the speed of sound in air. That is
Speed of sound in the rod = 19 × speed of sound in air.
Also, from the question,
Speed of sound in air is 347 m/s
∴ Speed of sound in the rod = 19 × 347 m/s
Speed of sound in the rod = 6593 m/s
The length of the rod will be the distance covered by the sound.
From
Speed = Distance / Time
Then, Distance = Speed × Time
From the question,
The woman hears the sound of the blow twice with a 0.19 s interval between and one sound comes through the rod and the other comes through the air.
That is, if the woman hears the sound that comes through the rod at time t seconds, then she hears the sound that comes through the air at time t+0.19 seconds.
For the sound through the rod
Speed = 6593 m/s
t = t secs
From
Distance = Speed × Time
∴ Distance covered by sound through the rod = 6593 m/s × t secs
= 6593t m
For the sound through the air
Speed = 347 m/s
t = t + 0.19 secs
∴ Distance covered by sound through the air = 347 m/s × (t+0.19) secs
= 347t + 65.93 m
Since the distance covered by sound through the rod and the distance covered by the sound through the air is the same, then we can write that
6593t = 347t + 65.93
6593t - 347t = 65.93
6246t = 65.93
t = 65.93/6246
t = 0.010556 s
This is the time she hears the sound from the rod.
Now, we can determine the distance covered by sound through the rod
Distance covered by sound through the rod = 6593 m/s × t secs
∴ Distance covered by sound through the rod = 6593 m/s × 0.010556 secs
Distance covered by sound through the rod = 69.6 m
Since the distance covered by sound through the rod gives the length of the rod,
Hence, the length of the rod is 69.6 m.
