Given the information which statements are true or false?

We know that when we pluck a string on an instrument the resulting sound wave travels through the air at a speed of (about) 344 m/s. But the wave moving on the STRING itself doesn't have to travel at 344 m/s. Let's consider some of the things that affect the velocity of a standing wave on a string.

A) The velocity of a wave traveling on a guitar string is increased if you exchange the string for one that is denser (keeping the length and tension unchanged.)
B) The velocity of the wave traveling on a string is higher if you pluck the string with a slightly larger sideways force
C) Given that waves travel on a guitar string with speed less than the speed of sound in air, and that a guitar string vibrates with frequency f: (T or F) the fundamental frequency of sound waves produced by this guitar will be equal to f.
D) Given that waves travel on a mandolin string with speed less than the speed of sound in air, and that a mandolin string vibrates with a wavelength lambda: (T or F) the resulting sound wave produced in the air will have a wavelength longer than lambda.
E) The velocity of the wave traveling on a string stays the same if you increase the length of the string (keeping the type of string, and the tension of the string, unchanged)

well, four of the above are ridculous. What do you think?

Well I think it is TFFF?

ACTUALLY IS IT TFFFT?

NOPE ITS NOT THAT EITHER!

To determine the truth or falsehood of each statement, let's analyze them one by one:

A) The velocity of a wave traveling on a guitar string is increased if you exchange the string for one that is denser (keeping the length and tension unchanged).

To understand this, we need to know the equation that relates wave velocity, frequency, and wavelength. The equation is:

Velocity = Frequency x Wavelength

Therefore, if we keep the frequency and tension of the string unchanged and replace it with a denser string, the wavelength will decrease. As a result, the velocity of the wave on the string will increase. So, statement A is True.

B) The velocity of the wave traveling on a string is higher if you pluck the string with a slightly larger sideways force.

The velocity of a wave traveling on a string is determined by the tension and mass per unit length of the string, not by the plucking force. So, statement B is False.

C) The fundamental frequency of sound waves produced by a guitar string will be equal to f.

Since the waves on a guitar string travel at a speed less than the speed of sound in air, the fundamental frequency of the string (the frequency of the first harmonic) will not be equal to the frequency at which the string vibrates. Therefore, statement C is False.

D) The resulting sound wave produced in the air by a mandolin string will have a wavelength longer than lambda.

When a wave travels from a denser medium (the string) to a less dense medium (air), its wavelength increases, while its velocity decreases. Therefore, the resulting sound wave produced in the air will have a longer wavelength than the wavelength of the mandolin string. So, statement D is True.

E) The velocity of the wave traveling on a string stays the same if you increase the length of the string (keeping the type of string and the tension of the string unchanged).

The velocity of a wave on a string is determined by the tension and mass per unit length of the string. Increasing the length of the string while keeping the tension and type of string unchanged will result in an increase in mass per unit length. Therefore, the velocity of the wave on the string will decrease. So, statement E is False.