How to generate correct sine wave

hello, I want to make the sine wave

when I execute below code at frequency 2, It is success.

but when I change the frequency to 10, It is not Sine wave..

What's wrong my code??

== correct ==

fs = 50;
t = 0:1/fs:1-1/fs;
x = sin(2*pi*2*t);
plot(t,x)

== non-correct

fs = 50;
t = 0:1/fs:1-1/fs;
x = sin(2*pi*10*t);
plot(t,x)

Answer 1

[Torsten]

fs = 500;
t = 0:1/fs:1-1/fs;
x = sin(2*pi*10*t);
plot(t,x)

Better ?

[제 허]

Thank you for your answer

I think that frequency of sin(2*pi*10*t) is 10.

if I take the frequency more than 20 frequency for Nyquist Theory, Its perfectly reconstruct sine wave.

It's right??

Answer 2

[Kevin Holly]

== correct ==

fs = 50;
t = 0:1/fs:1-1/fs;
x = sin(2*pi*2*t);
plot(t,x)

== non-correct

 fs = 50;
 t = 0:1/fs:1-1/fs;
 x = sin(2*pi*10*t);
 plot(t,x)

Corrected

 fs = 500;
 t = 0:1/fs:1-1/fs; %Increase the sample rate
 x = sin(2*pi*10*t);
 plot(t,x)

Your sampling freqency needs to be twice the size of the highest frequency you are detecting. See Nyquist Theorem.

[Stephen23]

"Your sampling freqency needs to be at least twice..."

[제 허]

Thank you for your answer.

I think that max frequency of sin(2*pi*10*t) is 10, then Its enough Fs = 20 for Nyquist Theorem.

It's right??

[Kevin Holly]

Correct.

[제 허]

Thank you for your answer

Then

fs = 50;

t = 0:1/fs:1-1/fs;

x = sin(2*pi*10*t);

plot(t,x)

In this code, The max frequency is 10, and sampling frequency is more than 5 times at 10

It satisfies the Nyquist Theory

but result of plot(t,x) is not like sine wave..

What's wrong??

[Kevin Holly]

Sorry about that, I missed the 2*pi.

subplot(2,1,1)
 fs = 20;
 t = 0:1/fs:1-1/fs;
 x = sin(2*pi*10*t);
 plot(t,x)


subplot(2,1,2)
fs = 2*pi*20;
t = 0:1/fs:1-1/fs;
x = sin(2*pi*10*t);
plot(t,x)

[제 허]

Sorry,,,,, I cant understand yet.

I dont know why Fs(sampling frequency) is multiplied by 2*pi ..

Thank you for your answer steadily