A female orb spider has a mass of 0.50 g. She is suspended...

Name: Problem 61, Chapter 15: College Physics: A Strategic Approach
Uploaded: 2020-11-08T14:26:33-08:00
Duration: 3 min 43 s
Channel: Sheh Lit Chang
Description: A female orb spider has a mass of 0.50 g. She is suspended from a tree branch by a 1.1 m length of 0.0020-mm-diameter silk. Spider silk has a density of 1300 kg/m3 . If you tap the branch and send a vibration down the thread, how long does it take to reach the spider?

A female orb spider has a mass of 0.50 g. She is suspended from a tree branch by a 1.1 m length of 0.0020-mm-diameter silk. Spider silk has a density of 1300 kg/m3 . If you tap the branch and send a vibration down the thread, how long does it take to reach the spider?

Key Concepts

Wave Propagation in a Stretched String

This concept deals with how disturbances travel through a medium like a string under tension. The speed at which a wave travels is determined by the interplay between the tension in the string and its linear mass density. Understanding this principle is essential when studying how vibrations or pulses move in flexible mediums.

Tension in a Suspended System

In scenarios where an object is suspended by a string, the tension is primarily due to the object's weight, which is the product of its mass and gravitational acceleration. This tension provides the restoring force that allows waves to propagate along the string and is critical for determining the speed of those waves.

Linear Density of a Medium

Linear density represents the mass per unit length of a material. It is a derived quantity obtained by dividing the mass density of the material by its cross-sectional area. This parameter is key to determining the wave speed, as a higher mass per unit length typically leads to slower wave propagation in the medium.

Wave Speed Equation

The wave speed in a string is given by the square root of the ratio between the tension in the string and its linear density. This equation links the physical properties of the medium—how tightly it is stretched (tension) and how much mass it has per unit length (linear density)—to the rate at which vibrations or disturbances can travel along the string.

Time-of-Flight Calculation

Once the wave speed in the medium is known, the time required for the wave to travel a certain distance can be calculated by dividing that distance by the wave speed. This basic relationship between distance, speed, and time is fundamental in analyzing the dynamics of wave propagation in any medium.

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